Fingered growth in channel geometry: A Loewner equation approach
arXiv:0801.1349 · doi:10.1103/PhysRevE.77.041602
Abstract
A simple model of Laplacian growth is considered, in which the growth takes place only at the tips of long, thin fingers. In a recent paper, Carleson and Makarov used the deterministic Loewner equation to describe the evolution of such a system. We extend their approach to a channel geometry and show that the presence of the side walls has a significant influence on the evolution of the fingers and the dynamics of the screening process, in which longer fingers suppress the growth of the shorter ones.
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